User:Editeur24/derivative

A derivative is not always a slope. Consider thi example f: \R \rightarrow \{0,1\}:

f(x) = 0 if x is rational f(x) =1 if x is irrational

f is discontinuous at all rational x. It is continuous and differnetiable at all irrational x. It does not have a slope anywhere.

Is this correct? Source or proof? Ask Chris Connell.